1. Field of the Invention
The present invention relates to a method of monitoring a change in thickness of a conductive film formed on a surface of a substrate during polishing and also relates to a polishing apparatus.
2. Description of the Related Art
A polishing apparatus is widely used for polishing a conductive film, such as a barrier film and an interconnect metal film, formed on a surface of a wafer. Polishing end point detection and a change in polishing conditions during polishing are determined based on a thickness of the conductive film. Thus, the polishing apparatus usually includes a film-thickness detector for detecting a thickness of the conductive film during polishing. A typical example of this film-thickness detector is an eddy current sensor. This eddy current sensor is configured to supply a high-frequency alternating current to a coil so as to induce an eddy current in the conductive film to thereby detect the thickness of the conductive film from a change in impedance caused by a magnetic field of the eddy current induced.
FIG. 1 is a view showing an equivalent circuit for explaining a principle of the eddy current sensor. When an AC power supply sends a high-frequency alternating current I1 to a coil 1, magnetic lines of force, induced in the coil 1, pass through the conductive film. As a result, mutual inductance occurs between a sensor-side circuit and a conductive-film-side circuit, and an eddy current I2 flows through the conductive film. This eddy current I2 creates magnetic lines of force, which cause a change in an impedance of the sensor-side circuit. The eddy current sensor measures the thickness of the conductive film from the change in the impedance of the sensor-side circuit.
In the sensor-side circuit and the conductive film-side circuit in FIG. 1, the following equations hold.R1I1+L1dI1/dt+MdI2/dt=E  (1)R2I2+L2dI2/dt+MdI1/dt=0  (2)
where M represents mutual inductance, R1 represents equivalent resistance of the sensor-side circuit including the coil 1, L1 represents self inductance of the sensor-side circuit including the coil 1, R2 represents equivalent resistance corresponding to eddy current loss, and L2 represents self inductance of the conductive film through which the eddy current flows.
Letting In=Anejωt (sine wave), the above equations (1) and (2) are expressed as follows.(R1+jωL1)I1+jωMI2=E  (3)(R2+jωL2)I2+jωMI1=E  (4)
From these equations (3) and (4), the following equations are derived.
                                                                        I                1                            =                            ⁢                                                E                  ⁡                                      (                                                                  R                        2                                            +                                              j                        ⁢                                                                                                  ⁢                        ω                        ⁢                                                                                                  ⁢                                                  L                          2                                                                                      )                                                  /                                  [                                                                                    (                                                                              R                            1                                                    +                                                      j                            ⁢                                                                                                                  ⁢                            ω                            ⁢                                                                                                                  ⁢                                                          L                              1                                                                                                      )                                            ⁢                                              (                                                                              R                            2                                                    +                                                      j                            ⁢                                                                                                                  ⁢                            ω                            ⁢                                                                                                                  ⁢                                                          L                              2                                                                                                      )                                                              +                                                                  ω                        2                                            ⁢                                              M                        2                                                                              ]                                                                                                        =                            ⁢                              E                /                                  [                                                            (                                                                        R                          1                                                +                                                  j                          ⁢                                                                                                          ⁢                          ω                          ⁢                                                                                                          ⁢                                                      L                            1                                                                                              )                                        +                                                                  ω                        2                                            ⁢                                                                        M                          2                                                /                                                  (                                                                                    R                              2                                                        +                                                          j                              ⁢                                                                                                                          ⁢                              ω                              ⁢                                                                                                                          ⁢                                                              L                                2                                                                                                              )                                                                                                      ]                                                                                        (        5        )            
Thus, the impedance Φ of the sensor-side circuit is given by the following equation.
                                                        Φ              =                            ⁢                              E                /                                  I                  1                                                                                                        =                            ⁢                                                [                                                            R                      1                                        +                                                                  ω                        2                                            ⁢                                              M                        2                                            ⁢                                                                        R                          2                                                /                                                  (                                                                                    R                              2                              2                                                        +                                                                                          ω                                2                                                            ⁢                                                              L                                2                                2                                                                                                              )                                                                                                      ]                                +                                                                                                      ⁢                              jω                ⁡                                  [                                                            L                      1                                        -                                                                  ω                        2                                            ⁢                                              L                        2                                            ⁢                                                                        M                          2                                                /                                                  (                                                                                    R                              2                              2                                                        +                                                                                          ω                                2                                                            ⁢                                                              L                                2                                2                                                                                                              )                                                                                                      ]                                                                                        (        6        )            
Substituting X and Y respectively for a real part (i.e., a resistance component) and an imaginary part (i.e., an inductive reactance component) of the impedance Φ, the above equation (6) is expressed as follows.Φ=X+jωY  (7)
FIG. 2 is a view showing a graph drawn by plotting X and Y, which change with a polishing time, on a XY coordinate system. The coordinate system shown in FIG. 2 is defined by a vertical axis as a Y-axis and a horizontal axis X-axis. Coordinates of a point T∞ are values of X and Y when a thickness of a film is zero, i.e., R2 is infinity. Where electrical conductivity of a substrate can be neglected, coordinates of a point T0 are values of X and Y when the thickness of the film is zero, i.e., R2 is infinity. A point Tn, specified by the values of X and Y, travels in an arc toward the point T0 as the thickness of the film decreases. A symbol k in FIG. 2 represents coupling coefficient, and the following relationship holds.M=k(L1L2)1/2  (8)
FIG. 3 shows a graph obtained by rotating the graph in FIG. 2 through 90 degrees in a counterclockwise direction and further translating the resulting graph. Specifically, the point specified by the coordinates (X, Y) is rotated about the origin O in the XY coordinate system, and the rotated coordinates are further moved so as to create a graph in which a distance between the origin O and the point specified by the coordinates (X, Y) decreases in accordance with an decrease in thickness of the film. A further process, such as amplification, may be applied to the graph in FIG. 3. Although FIG. 3 shows the case where the graph in FIG. 2 is rotated through 90 degrees in the counterclockwise direction, the rotation angle is not limited to 90 degrees. For example, the rotation angle can be adjusted such that the Y-coordinate corresponding to an upper limit of the film thickness to be monitored is equal to the Y-coordinate of the point where the film thickness is zero.
As shown in FIG. 3, the point Tn, positioned from the values of X and Y, travels in an arc toward the point T0, as the thickness of the film decreases. During traveling, a distance Z (=(X2+Y2)1/2) between the origin O in the X-Y coordinate system and the point Tn decreases as the thickness of the film decreases, as long as the point Tn is not positioned near the point T∞. Therefore, by monitoring the distance Z, a change in thickness of the film during polishing and a polishing end point can be determined. FIG. 4 shows a graph created by plotting the distance Z on the vertical axis and a polishing time on the horizontal axis. As shown in this graph, the distance Z decreases with the polishing time, and becomes constant at a certain time point. Thus, by detecting such a singular point of the distance Z, the polishing end point can be determined.
However, values of an output signal of the eddy current sensor could be drifted (i.e., moved parallel to each other), as shown by a dotted line in FIG. 5, due to a change in operating environments including an ambient temperature around the eddy current sensor and liquid permeation into a polishing pad, and due to a change in condition of the eddy current sensor itself with time. Drift of the values of the output signal of the eddy current sensor results in a change in distance Z from the origin O and an upward displacement of the graph itself, as shown in FIG. 6. Even in this case, it is possible to detect the polishing end point since the singular point is drifted as well. However, this output drift leads to problems when stopping polishing or when changing the polishing conditions at a time point when a preset target thickness is reached. This is because of a change in relationship between the values of the output signal of the eddy current sensor and the film thickness. This causes an error in detection of the polishing time.
Such drift of the output values of the eddy current sensor also affects other method of monitoring a film thickness, other than the above-described method based on the distance Z. For example, the Japanese laid-open patent application No. 2005-121616 discloses, in FIG. 13 thereof, a method of monitoring a change in film thickness during polishing based on a change in angle (θ) between a reference line passing through a center point (fixed point) and a line connecting a point specified by the output signal (component X, component Y) of the eddy current sensor and the center point. This method has an advantage of accurate monitoring of the change in film thickness regardless of the change in thickness of a polishing pad. However, in this method also, the angle θ could change in accordance with the change with time in output values of the eddy current sensor. As a result, the relationship between the values of the output signal of the eddy current sensor and the film thickness could change.
To solve these problems, it is necessary to calibrate the eddy current sensor regularly. However, in order to calibrate the eddy current sensor, the polishing process should be stopped, and as a result, the availability of the polishing apparatus is lowered. For this reason, in a semiconductor mass production facility, calibration of the eddy current sensor cannot be carried out frequently.